Effects of Fiber Type and Size on the Heterogeneity of Oxygen Distribution in Exercising Skeletal Muscle

The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.     

Fundamental physical cellular constraints drive self‐organization of tissues

Morphogenesis is driven by small cell shape changes that modulate tissue organization. Apical surfaces of proliferating epithelial sheets have been particularly well studied. Currently, it is accepted that a stereotyped distribution of cellular polygons is conserved in proliferating tissues among metazoans. In this work, we challenge these previous findings showing that diverse natural packed tissues have very different polygon distributions. We use Voronoi tessellations as a mathematical framework that predicts this diversity. We demonstrate that Voronoi tessellations and the very different tissues analysed share an overriding restriction: the frequency of polygon types correlates with the distribution of cell areas. By altering the balance of tensions and pressures within the packed tissues using disease, genetic or computer model perturbations, we show that as long as packed cells present a balance of forces within tissue, they will be under a physical constraint that limits its organization. Our discoveries establish a new framework to understand tissue architecture in development and disease.     

Analysis of skeletal muscle capillarization: methodological problems

Capillarization of skeletal muscle has been studied on the same muscle with different methods. Capillary/muscle fibre ratio, number of muscle fibres in contact with capillaries, capillary density in a unit area, capillary density on the muscle fibre surface were determined. The various methods gave different numerical data. Determination of capillary/muscle fibre ratio seemed to be the most reliable index of the changes in pathological conditions.     

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

Numerical simulation of oxygen delivery to muscle tissue in the presence of hemoglobin-based oxygen carriers

This work represents a culmination of research on oxygen transport to muscle tissue, which takes into account oxygen transport due to convection, diffusion, and the kinetics of simultaneous reactions between oxygen and hemoglobin and myoglobin. The effect of adding hemoglobin-based oxygen carriers (HBOCs) to the plasma layer of blood in a single capillary surrounded by muscle tissue based on the geometry of the Krogh tissue cylinder is examined for a range of HBOC oxygen affinity, HBOC concentration, capillary inlet oxygen tension (pO(2)), and hematocrit. The full capillary length of the hamster retractor muscle was modeled under resting (V(max) = 1.57 x 10(-4) mLO(2) mL(-1) s(-1), cell velocity (v(c)) = 0.015 cm/s) and working (V(max) = 1.57 x 10(-3) mLO(2) mL(-1) s(-1), v(c) = 0.075 cm/s) conditions. Two spacings between the red blood cell (RBC) and the capillary wall were examined, corresponding to a capillary with and without an endothelial surface layer. Simulations led to the following conclusions, which lend physiological insight into oxygen transport to muscle tissue in the presence of HBOCs: (1) The reaction kinetics between oxygen and myoglobin in the tissue region, oxygen and HBOCs in the plasma, and oxygen and RBCs in the capillary lumen should not be neglected. (2) Simulation results yielded new insight into possible mechanisms of oxygen transport in the presence of HBOCs. (3) HBOCs may act as a source or sink for oxygen in the capillary and may compete with RBCs for oxygen. (4) HBOCs return oxygen delivery to muscle tissue to normal for varying degrees of hypoxia (inlet capillary pO(2) < 30 mmHg) and anemia (hematocrit < 46%) for the hamster model.     

A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport

The objective of this study was to investigate the effects of capillary network anastomoses and tortuosity on oxygen transport in skeletal muscle, as well as the importance of muscle fibers in determining the arrangement of parallel capillaries. Countercurrent flow and random capillary blockage (e.g. by white blood cells) were also studied. A general computational model was constructed to simulate oxygen transport from a network of blood vessels within a rectangular volume of tissue. A geometric model of the capillary network structure, based on hexagonally packed muscle fibers, was constructed to produce networks of straight unbranched capillaries, capillaries with anastomoses, and capillaries with tortuosity, in order to examine the effects of these geometric properties. Quantities examined included the tissue oxygen tension and the capillary oxyhemoglobin saturation. The computational model included a two-phase simulation of blood flow. Appropriate parameters were chosen for working hamster cheek-pouch retractor muscle. Our calculations showed that the muscle-fiber geometry was important in reducing oxygen transport heterogeneity, as was countercurrent flow. Tortuosity was found to increase tissue oxygenation, especially when combined with anastomoses. In the absence of tortuosity, anastomoses had little effect on oxygen transport under normal conditions, but significantly improved transport when vessel blockages were present.     

Mathematical modeling of oxygen transport in skeletal muscle

Inhomogeneous perfusion of capillary beds can result in large-scale diffusion of oxygen between distant portions of an organ. The conceptual model of a single capillary supplying oxygen to a surrounding concentric cylinder of tissue is not applicable to a consideration of such processes. An entirely different approach to the modeling of oxygen transport to tissue, with specific reference to the capillary beds of skeletal muscle, is presented here. This approach is intended to replace the theoretical Krogh cylinder model of capillary-tissue oxygen transport with a much more realistic model that takes into account inhomogeneities of capillary density, blood flow velocity, and oxygen concentration inherent in the micro-vasculature. The oxygen distribution in inhomogeneously perfused skeletal muscle is analyzed mathematically by defining an averaged concentration profile that neglects the fine-scale variation from capillary to capillary.     

Adaptations in skeletal muscle capillarity following changes in oxygen supply and changes in oxygen demands.

The effects of changes in oxygen supply and oxygen demands on fiber cross-sectional areas, capillary densities and capillary to fiber ratios were determined in three skeletal muscles of rat. The muscles examined were the vastus lateralis, soleus, and diaphragm. Reduced oxygen supply was produced by subjecting rats to ambient hypoxia, and increased oxygen demands were produced by subjecting rats to low ambient temperatures or treatment with thyroxin. Capillaries were visualized by injecting fluorescent dyes into the circulation. Muscles were quick frozen at resting lengths to preserve normal fiber geometry and were subsequently sectioned on a cryostat. All of the muscles sampled from animals in the experimental groups had elevated capillary densities. However, capillary to fiber ratios were not increased significantly in any muscle, for any experimental condition. Thus, all of the observed differences in capillarity were due to changes in the intrinsic rate of muscle fiber growth. Further, the relations of capillary density and capillary to fiber ratio to fiber area were the same as those obtained during normal maturation, suggesting that capillary growth is closely linked to the intrinsic rate of fiber growth.     

Temperature and angiogenesis: the possible role of mechanical factors in capillary growth

This review examines the effect of prolonged cold exposure on muscle capillary supply in mammals and fishes. In rats and hamsters, the response to a simulated onset of winter is to conserve the microcirculation and maintain a constant capillary to fibre ratio (C:F), implying either an unaltered vacular bed or angiogenesis matched by muscle hyperplasia, while chronic acclimation to low environmental temperature induces a variable degree of muscle atrophy, which in turn increases capillary density (CD). In striped bass and rainbow trout, cold-induced angiogenesis results in an increase in C:F, but also a cold-induced fibre hypertrophy that is accompanied by a powerful angiogenic response such that CD is much less sensitive to changes in fibre size. Endothelial cells can act as mechanotransducers such that angiogenesis may be initiated by changes in their physical environment. It is hypothesised that in mammals, the metabolic consequences of cold exposure increases the luminal shear stress, while in fishes the stimulus for angiogenesis is abluminal stretch following an increase in fibre size.     

A computational model of oxygen transport in skeletal muscle for sprouting and splitting modes of angiogenesis

Oxygen transport from capillary networks in muscle at a high oxygen consumption rate was simulated using a computational model to assess the relative efficacies of sprouting and splitting modes of angiogenesis. Efficacy was characterized by the volumetric fraction of hypoxic tissue and overall heterogeneity of oxygen distribution at steady state. Oxygen transport was simulated for a three-dimensional vascular network using parameters for rat extensor digitorum longus (EDL) muscle when oxygen consumption by tissue reached 6, 12, and 18 times basal consumption. First, a control network was generated by using straight non-anastomosed capillaries to establish baseline capillarity. Two networks were then constructed simulating either abluminal lateral sprouting or intraluminal splitting angiogenesis such that capillary surface area was equal in both networks. The sprouting network was constructed by placing anastomosed capillaries between straight capillaries of the control network with a higher probability of placement near hypoxic tissue. The splitting network was constructed by splitting capillaries from the control network into two branches at randomly chosen branching points. Under conditions of moderate oxygen consumption (6 times basal), only minor differences in oxygen delivery resulted between the sprouting and splitting networks. At higher consumption levels (12 and 18 times basal), the splitting network had the lowest volume of hypoxic tissue of the three networks. However, when total blood flow in all three networks was made equal, the sprouting network had the lowest volume of hypoxic tissue. This study also shows that under the steady-state conditions the effect of myoglobin (Mb) on oxygen transport was small.     

Oxygen dependence of metabolism and cellular adaptation in vertebrate muscles: a review

The key roles the cardiovascular system play in the complex distribution of blood, and consequently oxygen, have been extensively studied in vertebrates. Numerous studies have also revealed the complex and varied ways in which tissues cope with compromised oxygen supply. The links between these two processes are the subject of much current research. This article aims to review how blood supply influences tissue oxygenation and affects metabolism, and how this might have played a role in the evolution of the complex muscle arrangements which characterise vertebrates. Muscle tissue is the greatest proportion of body mass in most vertebrates and undergoes dramatic alterations in metabolism and associated oxygen flux. Special attention is given to the myotome of fishes, in which the partitioning of the fibre types contrasts with the mosaic arrangement of tetrapods. This gives us the opportunity to study pure whole vascularised muscle blocks, rather than single fibres, and further explore the interrelationship between oxygen supply and tissue energetics.     

Vascularization of the lateral muscle of some elasmobranchiomorph fishes

The vascular bed of the locomotor muscle in three shark species and in a holocephalan is investigated and the capillarization quantified by morphometrical methods. The red muscle fibres of Scyliorhinus, Galeus, Etmopterus and Chimaera are well vascularized having respectively 25, 18, 23 and 5 per cent of fibre surface covered by capillaries. The white muscle fibres of Scyliorhinus are far better vascularized than white muscle fibres of Galeus, Etmopterus and Chimaera . The fibre surface covered by capillaries are 9, 1.4, 0.2 and 1.3 per cent, respectively. The intermediate muscle fibres have a vascular supply between that of red and white muscle fibres in all species. If the capillary contact area to the fibres are related to the mitochondrial volume, more similar values are obtained for the vascular supply to all fibres types in all animals. This parameter indicates that there is a definite relation between the capacity of the oxygen transport system and the aerobic metabolic machinery.     

Oxygen delivery to skeletal muscle fibers: effects of microvascular unit structure and control mechanisms

The number of perfused capillaries in skeletal muscle varies with muscle activation. With increasing activation, muscle fibers are recruited as motor units consisting of widely dispersed fibers, whereas capillaries are recruited as groups called microvascular units (MVUs) that supply several adjacent fibers. In this study, a theoretical model was used to examine the consequences of this spatial mismatch between the functional units of muscle activation and capillary perfusion. Diffusive oxygen transport was simulated in cross sections of skeletal muscle, including several MVUs and fibers from several motor units. Four alternative hypothetical mechanisms controlling capillary perfusion were considered. First, all capillaries adjacent to active fibers are perfused. Second, all MVUs containing capillaries adjacent to active fibers are perfused. Third, each MVU is perfused whenever oxygen levels at its feed arteriole fall below a threshold value. Fourth, each MVU is perfused whenever the average oxygen level at its capillaries falls below a threshold value. For each mechanism, the dependence of the fraction of perfused capillaries on the level of muscle activation was predicted. Comparison of the results led to the following conclusions. Control of perfusion by MVUs increases the fraction of perfused capillaries relative to control by individual capillaries. Control by arteriolar oxygen sensing leads to poor control of tissue oxygenation at high levels of muscle activation. Control of MVU perfusion by capillary oxygen sensing permits adequate tissue oxygenation over the full range of activation without resulting in perfusion of all MVUs containing capillaries adjacent to active fibers.     

Simultaneous histochemical demonstration of capillaries and muscle fibre types

Immunohistochemical staining of fibronectin is proposed as a good method for demonstrating capillaries in skeletal muscle tissue. The reaction superimposed on the histochemical reaction for myofibrillar ATPase enables simultaneous demonstration of fibre typing and capillary supply on the same tissue section. The method is quick and makes possible automated image analysis.     

Alterations in the muscle-to-capillary interface in patients with different degrees of chronic obstructive pulmonary disease

Background

It is hypothesized that decreased capillarization of limb skeletal muscle is implicated in the decreased exercise tolerance in COPD patients. We have recently demonstrated decreased number of capillaries per muscle fibre (CAF) but no changes in CAF in relation to fibre area (CAFA), which is based on the diffusion distance between the capillary and muscle fibre. The aim of the current study is to investigate the muscle-to-capillary interface which is an important factor involved in oxygen supply to the muscle that has previously been suggested to be a more sensitive marker for changes in the capillary bed compared to CAF and CAFA.

Methods

23 COPD patients and 12 age-matched healthy subjects participated in the study. Muscle-to-capillary interface was assessed in muscle biopsies from the tibialis anterior muscle using the following parameters:1) The capillary-to-fibre ratio (C:F_i) which is defined as the sum of the fractional contributions of all capillary contacts around the fibre2) The ratio between C:F_i and the fibre perimeter (CFPE-index)3) The ratio between length of capillary and fibre perimeter (LC/PF) which is also referred to as the index of tortuosity.Exercise capacity was determined using the 6-min walking test.

Results

A positive correlation was found between CFPE-index and ascending disease severity with CFPE-index for type I fibres being significantly lower in patients with moderate and severe COPD. Furthermore, a positive correlation was observed between exercise capacity and CFPE-index for both type I and type IIa fibres.

Conclusion

It can be concluded that the muscle-to-capillary interface is disturbed in the tibialis anterior muscle in patients with COPD and that interface is strongly correlated to increased disease severity and to decreased exercise capacity in this patient group.     

Comparative aspects of fibre types,areas, and capillary supply in the pectoralis muscle of some passerine birds with differing migratory behaviour

Summary Fibre types, fibre areas and capillary supply in the pectoralis muscle of fifteen passerines with four different patterns of migratory behaviour have been studied. The predominant fibre type was a fast-twitch oxidative-glycolytic which was the only fibre type present in all species, except in the robin and the blackbird where a fast fibre with intermediate oxidative capacity and a fast glycolytic fibre were also found. There was a significant difference in fibre areas between birds with different migratory strategies, with the long-distance migratory group having the smallest fibres. This also led to higher capillary densities, shorter diffusion distances and, consequently, more capillaries around the fibres relative to fibre area in this group. This indicates an adaptation in the morphology of the pectoralis muscle to differences in migration strategies. In the robin, the proportion of the intermediate fibre was significantly greater during the breeding season than during migration. Seasonal differences in fibre areas and capillary supply within a species were also seen, but no definite trends were detectable.Abbreviations CC capillary/fibre contacts - CCA mean number of capillaries in contact with a fibre relative to fibre cross-sectional area - MD mean diffusion length - CD capillary density - FG fast-twich glycolytic - FOG fast-twitch oxidative-glycolytic     

Limits to the acclimation of fish muscle

Summary Some of the factors which lead to acclimational changes in fish axial muscle are reviewed and discussed: these are temperature, hypoxia, training and habitat. On the fine structural level, the morphological adaptations are seen mainly in mitochondrial and intracellular lipid content and capillary supply of swimming muscle. Cold acclimation, hypoxic conditions and an endurance training programme show a general trend for transition to more aerobic fibre types and a more aerobic type of muscle.     

On facilitated oxygen diffusion in muscle tissues.

The role of myoglobin in facilitated diffusion of oxygen in muscle in examined in a tissue model that utilizes a central supplying capillary and a tissue cylinder concentric with the central capillary, and that includes the nonlinear characteristics of the oxygen-hemoglobin dissociation reaction. In contrast to previous work, this model exhibits the effect of blood flow and a realistic, though ideal, tissue-capillary geometry. Solutions of the model equations are obtained by a singular-perturbation technique, and numerical results are discussed for model parameters of physiologic interest. In contrast to the findings of Murray, Rubinow, Taylor, and others, fractional order perturbation terms obtained for the "boundary-layer" regions near the supplying capillaries are quite significant in the overall interpretation of the modeling results. Some closed solutions are found for special cases, and these are contrasted with the full singular-perturbation solution. Interpretations are given for parameters of physiologic interest.     

Axial diffusion and wall permeability effects in perfused capillary-tissue structures

Attempts to experimentally examine oxygen supply and distribution in the isolated perfused heart and brain have renewed interest in mathematical models of artificially perfused capillary-tissue structures. The need to understand histograms of PO2 measurements from these isolated-perfused organ studies (modified Lagendorf preparations) has required that existing mathematical models and their boundary conditions be re-examined in the context of these experiments. A unifying system of equations and boundary conditions are examined here for the purpose of studying the effects of anisotropic diffusion, and capillary vessel wall permeability on both the capillary and tissue substrate supply. The mathematical models are explored for parameters of physiologic interest, and some comparisons are made with experimental determinations. The comparisons with data suggest an anisotropic transport of oxygen in the tissue that is unexplained by known physiologic mechanisms.